Question

In the accompanying diagram ab is tangent to circle O at B and ACD is a secant.

If AB=9 and AD=27, find AC

Answer 1

AC = 3

Explanation:

Based on tangent and secant theorem, thus:

AB² = AC × (AC + CD)

AB = 9

AD = AC + CD = 27

Plug in the values

9² = AC × (27)

81 = AC × 27

Divide both sides by 27

81/27 = AC

3 = AC

AC = 3